Components coming off an assembly line are either free of defects (S, for succes

Question

Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 80% of all such components are defect-free. Components are independently selected and tested one by one. Let y denote the number of components that must be tested until a defect-free component is obtained.

(b) Determine the probability of each of the five smallest y values. You should see a pattern that leads to a simple formula for P(y), the probability distribution of y.
P(y = 1) =   
P(y = 2) =  
P(y = 3) =  
P(y = 4) =   
P(y = 5) =  

Explanation / Answer

as this is geometric distribution for which P(y) =P(no success till y-1 values and success on yth event)

=(1-0.8)y-1*0.8

frm above

P(Y=1) =0.8

P(Y=2)=0.2*0.8=0.16

P(Y=3)=0.22*0.8 =0.032

P(Y=4)=0.23*0.8 =0.0064

P(Y=5)=0.24*0.8 =0.00128

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